{"id":278941,"date":"2025-08-02T13:24:03","date_gmt":"2025-08-02T13:24:03","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=278941"},"modified":"2025-08-02T13:24:05","modified_gmt":"2025-08-02T13:24:05","slug":"frac","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/02\/frac\/","title":{"rendered":"Frac"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/image-199.png\" alt=\"\" class=\"wp-image-278942\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer to the expression is&nbsp;<strong>-2^(43\/2)<\/strong>.<\/p>\n\n\n\n<p>The problem requires simplifying the expression 2^25 \/ (-\u221a2)^7. To solve this, we can break it down into a few key steps, focusing on simplifying the denominator first and then applying the rules of exponents.<\/p>\n\n\n\n<p>First, let&#8217;s address the denominator, which is (-\u221a2)^7. When a negative number is raised to an odd power, the result is negative. Therefore, (-\u221a2)^7 is equal to -(\u221a2)^7. This isolates the negative sign, which we will carry through the calculation.<\/p>\n\n\n\n<p>Next, we simplify (\u221a2)^7. The square root of 2, or \u221a2, can be written in exponential form as 2^(1\/2). So, (\u221a2)^7 is the same as (2^(1\/2))^7. Using the power of a power rule for exponents, which states that (a^m)^n = a^(m*n), we multiply the exponents. This gives us 2^((1\/2) * 7), which simplifies to 2^(7\/2). Combining this with the negative sign from earlier, the entire denominator, (-\u221a2)^7, simplifies to -2^(7\/2).<\/p>\n\n\n\n<p>Now, we can substitute this simplified denominator back into the original expression. The problem becomes 2^25 \/ (-2^(7\/2)).<\/p>\n\n\n\n<p>Finally, we perform the division. A positive number divided by a negative number results in a negative answer. We apply the quotient rule for exponents, which states that a^m \/ a^n = a^(m-n). In our case, this means we subtract the exponent in the denominator from the exponent in the numerator: 25 &#8211; 7\/2. To perform this subtraction, we find a common denominator, converting 25 to 50\/2. The calculation is 50\/2 &#8211; 7\/2 = 43\/2.<\/p>\n\n\n\n<p>Combining the negative sign and the new exponent, the final simplified answer is -2^(43\/2).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/learnexams-banner5-101.jpeg\" alt=\"\" class=\"wp-image-278943\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct answer to the expression is&nbsp;-2^(43\/2). The problem requires simplifying the expression 2^25 \/ (-\u221a2)^7. To solve this, we can break it down into a few key steps, focusing on simplifying the denominator first and then applying the rules of exponents. First, let&#8217;s address the denominator, which is [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-278941","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/278941","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=278941"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/278941\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=278941"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=278941"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=278941"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}